Path generation for static obstacle avoidance

ABSTRACT

A method of generating a path for an autonomous driving vehicle (ADV) includes obtaining a plurality of path inputs including a lateral and a longitudinal starting state, a threshold lateral jerk, and a set of static obstacle boundaries with respect to a reference line, obtaining a plurality of path constraints related to the threshold lateral jerk, avoidance of static obstacles, and a threshold lateral velocity, obtaining a cost function associated with a path objective, the cost function comprising first, second, and third terms relating to cumulative lateral distances, to cumulative first order lateral rates of change, and to cumulative second order lateral rates of change, respectively, generating a plurality of planned ADV states as path results based on the plurality of path inputs, the plurality of path constraints, and the cost function and generating control signals to control the ADV based on the plurality of planned ADV states.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to operatingautonomous vehicles. More particularly, embodiments of the disclosurerelate to generating a path with static obstacle avoidance.

BACKGROUND

Vehicles operating in an autonomous mode (e.g., driverless) can relieveoccupants, especially the driver, from some driving-relatedresponsibilities. When operating in an autonomous mode, the vehicle cannavigate to various locations using onboard sensors, allowing thevehicle to travel with minimal human interaction or in some caseswithout any passengers.

Motion planning and control are critical operations in autonomousdriving. A path describes the geometric shape of the movement forautonomous vehicles. Various factors affect the desirability of anygiven path, including those relating to passenger comfort and safety.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure are illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 is a block diagram illustrating a networked system according toone embodiment.

FIG. 2 is a block diagram illustrating an example of an autonomousvehicle according to one embodiment.

FIGS. 3A-3B are block diagrams illustrating an example of a perceptionand planning system used with an autonomous vehicle according to oneembodiment.

FIG. 4 is a diagram illustrating a vehicle position under anSL-coordinate system under an XY plane according to one embodiment.

FIG. 5 is a diagram illustrating an example method for obtainingdiscretized obstacle boundaries under the SL-coordinate system accordingto one embodiment.

FIG. 6 is a block diagram illustrating various example componentsinvolved in the path planning process according to one embodiment.

FIG. 7 is a flowchart illustrating an example method for planning a pathfor an ADV according to one embodiment.

FIG. 8 is a diagram illustrating an example method for determining apath for an ADV under the SL-coordinate system according to oneembodiment.

FIG. 9 is a flowchart illustrating an example method for planning a pathfor an ADV according to one embodiment.

FIG. 10 is a block diagram illustrating a data processing systemaccording to one embodiment.

DETAILED DESCRIPTION

Various embodiments and aspects of the disclosures will be describedwith reference to details discussed below, and the accompanying drawingswill illustrate the various embodiments. The following description anddrawings are illustrative of the disclosure and are not to be construedas limiting the disclosure. Numerous specific details are described toprovide a thorough understanding of various embodiments of the presentdisclosure. However, in certain instances, well-known or conventionaldetails are not described in order to provide a concise discussion ofembodiments of the present disclosures.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin conjunction with the embodiment can be included in at least oneembodiment of the disclosure. The appearances of the phrase “in oneembodiment” in various places in the specification do not necessarilyall refer to the same embodiment.

Some embodiments relate to a method, apparatus, and system forgenerating an path for an autonomous driving vehicle (ADV), taking intoaccount the comfort level associated with the path as well as thepreference for the path to stay close to the lane center line and awayfrom obstacles with a buffer. In particular, a path planner generate aplurality of planned autonomous driving vehicle (ADV) states withnonlinear optimization based on a plurality of path inputs, a pluralityof path constraints, and a cost function. The planned ADV states maythen be used to generate control signals to control the ADV.

In one embodiment, path inputs including an ADV lateral starting state,an ADV longitudinal starting state, a threshold lateral jerk, and staticobstacle boundaries with respect to a reference line are received at thepath planner. A set of path constraints including constraints relatingto the threshold lateral jerk, avoidance of one or more staticobstacles, and a threshold lateral velocity are received. A costfunction associated with a path objective and comprising a first termrelating to cumulative lateral distances, a second term relating tocumulative first order lateral rates of change, and a third termrelating to cumulative second order lateral rates of change is received.Thereafter, a plurality of planned ADV states are generated as pathresults with nonlinear optimization, where the path results minimize avalue of the cost function while satisfying or meeting the set of pathconstraints. Control signals are then generated to control the ADV basedon the plurality of planned ADV states.

In one embodiment, a station-lateral (SL)-coordinate system including alongitudinal dimension and a lateral dimension is utilized, where thelongitudinal dimension is along a tangential direction of the referenceline, and the lateral dimension is perpendicular to the longitudinaldimension. The longitudinal dimension in the SL space represents alongitudinal distance of a particular object from a current location ofthe vehicle that is presumably drives along the reference line. Thelateral dimension in the SL space represents the shortest distancebetween the object and the reference line at a particular time orlocation represented by the longitudinal dimension. Such a graph in theSL space is referred to as an SL graph.

In one embodiment, each of the ADV lateral starting state and theplurality of planned ADV states include a lateral distance, a firstorder lateral rate of change, and a second order lateral rate of change.In one embodiment, the first order lateral rate of change is a rate ofchange of the lateral distance with respect to change of longitudinaldistance, and the second order lateral rate of change is a rate ofchange of the first order lateral rate of change with respect to changeof longitudinal distance.

In one embodiment, the ADV longitudinal starting state may include alongitudinal distance, a first order longitudinal rate of change, and asecond order longitudinal rate of change. In one embodiment, the firstorder longitudinal rate of change is a rate of change of thelongitudinal distance with respect to change in time, and the secondorder lateral rate of change is a rate of change of the first orderlateral rate of change with respect to change of longitudinal distance.

In one embodiment, the cost function further includes a first weightassociated with the first term, a second weight associated with thesecond term, and a third weight associated with the third term. In oneembodiment, the plurality of planned ADV states correspond todiscretized points along the reference line spaced by a uniformlongitudinal distance discretization resolution between a beginningpoint and an ending point of the reference line under consideration. Inone embodiment, the plurality of path inputs further comprise a targetADV ending state.

FIG. 1 is a block diagram illustrating an autonomous vehicle networkconfiguration according to one embodiment of the disclosure. Referringto FIG. 1, network configuration 100 includes autonomous vehicle 101that may be communicatively coupled to one or more servers 103-104 overa network 102. Although there is one autonomous vehicle shown, multipleautonomous vehicles can be coupled to each other and/or coupled toservers 103-104 over network 102. Network 102 may be any type ofnetworks such as a local area network (LAN), a wide area network (WAN)such as the Internet, a cellular network, a satellite network, or acombination thereof, wired or wireless. Server(s) 103-104 may be anykind of servers or a cluster of servers, such as Web or cloud servers,application servers, backend servers, or a combination thereof. Servers103-104 may be data analytics servers, content servers, trafficinformation servers, map and point of interest (MPOI) servers, orlocation servers, etc.

An autonomous vehicle refers to a vehicle that can be configured to inan autonomous mode in which the vehicle navigates through an environmentwith little or no input from a driver. Such an autonomous vehicle caninclude a sensor system having one or more sensors that are configuredto detect information about the environment in which the vehicleoperates. The vehicle and its associated controller(s) use the detectedinformation to navigate through the environment. Autonomous vehicle 101can operate in a manual mode, a full autonomous mode, or a partialautonomous mode. Hereinafter the terms “autonomous vehicle” and“autonomous driving vehicle” (ADV) may be used interchangeably.

In one embodiment, autonomous vehicle 101 includes, but is not limitedto, perception and planning system 110, vehicle control system 111,wireless communication system 112, user interface system 113,infotainment system 114, and sensor system 115. Autonomous vehicle 101may further include certain common components included in ordinaryvehicles, such as, an engine, wheels, steering wheel, transmission,etc., which may be controlled by vehicle control system 111 and/orperception and planning system 110 using a variety of communicationsignals and/or commands, such as, for example, acceleration signals orcommands, deceleration signals or commands, steering signals orcommands, braking signals or commands, etc.

Components 110-115 may be communicatively coupled to each other via aninterconnect, a bus, a network, or a combination thereof. For example,components 110-115 may be communicatively coupled to each other via acontroller area network (CAN) bus. A CAN bus is a vehicle bus standarddesigned to allow microcontrollers and devices to communicate with eachother in applications without a host computer. It is a message-basedprotocol, designed originally for multiplex electrical wiring withinautomobiles, but is also used in many other contexts.

Referring now to FIG. 2, in one embodiment, sensor system 115 includes,but it is not limited to, one or more cameras 211, global positioningsystem (GPS) unit 212, inertial measurement unit (IMU) 213, radar unit214, and a light detection and range (LIDAR) unit 215. GPS system 212may include a transceiver operable to provide information regarding theposition of the autonomous vehicle. IMU unit 213 may sense position andorientation changes of the autonomous vehicle based on inertialacceleration. Radar unit 214 may represent a system that utilizes radiosignals to sense objects within the local environment of the autonomousvehicle. In some embodiments, in addition to sensing objects, radar unit214 may additionally sense the speed and/or heading of the objects.LIDAR unit 215 may sense objects in the environment in which theautonomous vehicle is located using lasers. LIDAR unit 215 could includeone or more laser sources, a laser scanner, and one or more detectors,among other system components. Cameras 211 may include one or moredevices to capture images of the environment surrounding the autonomousvehicle. Cameras 211 may be still cameras and/or video cameras. A cameramay be mechanically movable, for example, by mounting the camera on arotating and/or tilting a platform.

Sensor system 115 may further include other sensors, such as, a sonarsensor, an infrared sensor, a steering sensor, a throttle sensor, abraking sensor, and an audio sensor (e.g., microphone). An audio sensormay be configured to capture sound from the environment surrounding theautonomous vehicle. A steering sensor may be configured to sense thesteering angle of a steering wheel, wheels of the vehicle, or acombination thereof. A throttle sensor and a braking sensor sense thethrottle position and braking position of the vehicle, respectively. Insome situations, a throttle sensor and a braking sensor may beintegrated as an integrated throttle/braking sensor.

In one embodiment, vehicle control system 111 includes, but is notlimited to, steering unit 201, throttle unit 202 (also referred to as anacceleration unit), and braking unit 203. Steering unit 201 is to adjustthe direction or heading of the vehicle. Throttle unit 202 is to controlthe speed of the motor or engine that in turn control the speed andacceleration of the vehicle. Braking unit 203 is to decelerate thevehicle by providing friction to slow the wheels or tires of thevehicle. Note that the components as shown in FIG. 2 may be implementedin hardware, software, or a combination thereof.

Referring back to FIG. 1, wireless communication system 112 is to allowcommunication between autonomous vehicle 101 and external systems, suchas devices, sensors, other vehicles, etc. For example, wirelesscommunication system 112 can wirelessly communicate with one or moredevices directly or via a communication network, such as servers 103-104over network 102. Wireless communication system 112 can use any cellularcommunication network or a wireless local area network (WLAN), e.g.,using WiFi to communicate with another component or system. Wirelesscommunication system 112 could communicate directly with a device (e.g.,a mobile device of a passenger, a display device, a speaker withinvehicle 101), for example, using an infrared link, Bluetooth, etc. Userinterface system 113 may be part of peripheral devices implementedwithin vehicle 101 including, for example, a keyboard, a touch screendisplay device, a microphone, and a speaker, etc.

Some or all of the functions of autonomous vehicle 101 may be controlledor managed by perception and planning system 110, especially whenoperating in an autonomous driving mode. Perception and planning system110 includes the necessary hardware (e.g., processor(s), memory,storage) and software (e.g., operating system, planning and routingprograms) to receive information from sensor system 115, control system111, wireless communication system 112, and/or user interface system113, process the received information, plan a route or path from astarting point to a destination point, and then drive vehicle 101 basedon the planning and control information. Alternatively, perception andplanning system 110 may be integrated with vehicle control system 111.

For example, a user as a passenger may specify a starting location and adestination of a trip, for example, via a user interface. Perception andplanning system 110 obtains the trip related data. For example,perception and planning system 110 may obtain location and routeinformation from an MPOI server, which may be a part of servers 103-104.The location server provides location services and the MPOI serverprovides map services and the POIs of certain locations. Alternatively,such location and MPOI information may be cached locally in a persistentstorage device of perception and planning system 110.

While autonomous vehicle 101 is moving along the route, perception andplanning system 110 may also obtain real-time traffic information from atraffic information system or server (TIS). Note that servers 103-104may be operated by a third party entity. Alternatively, thefunctionalities of servers 103-104 may be integrated with perception andplanning system 110. Based on the real-time traffic information, MPOIinformation, and location information, as well as real-time localenvironment data detected or sensed by sensor system 115 (e.g.,obstacles, objects, nearby vehicles), perception and planning system 110can plan a path or a route, and drive vehicle 101, for example, viacontrol system 111, according to the planned route to reach thespecified destination safely and efficiently.

Server 103 may be a data analytics system to perform data analyticsservices for a variety of clients. In one embodiment, data analyticssystem 103 includes data collector 121 and machine learning engine 122.Data collector 121 collects driving statistics 123 from a variety ofvehicles, either autonomous vehicles or regular vehicles driven by humandrivers. Driving statistics 123 include information indicating thedriving commands (e.g., throttle, brake, steering commands) issued andresponses of the vehicles (e.g., speeds, accelerations, decelerations,directions) captured by sensors of the vehicles at different points intime. Driving statistics 123 may further include information describingthe driving environments at different points in time, such as, forexample, routes (including starting and destination locations), MPOIs,road conditions, weather conditions, etc.

Based on driving statistics 123, machine learning engine 122 generatesor trains a set of rules, algorithms, and/or predictive models 124 for avariety of purposes. In one embodiment, algorithms 124 may include anpath algorithm that receives inputs, constraints, and a cost function,and generates an path for the ADV, taking into account the comfort levelassociated with the path as well as the preference for the path to stayclose to the lane center line and away from obstacles with a buffer. Acost function for the path planning may also be generated as a part ofalgorithms 124. Algorithms 124 can then be uploaded on ADVs to beutilized during autonomous driving in real-time.

FIGS. 3A and 3B are block diagrams illustrating an example of aperception and planning system used with an autonomous vehicle accordingto one embodiment. System 300 may be implemented as a part of autonomousvehicle 101 of FIG. 1 including, but is not limited to, perception andplanning system 110, control system 111, and sensor system 115.Referring to FIGS. 3A-3B, perception and planning system 110 includes,but is not limited to, localization module 301, perception module 302,prediction module 303, decision module 304, planning module 305, controlmodule 306, routing module 307, static obstacle mapper 308, path planner309.

Some or all of modules 301-309 may be implemented in software, hardware,or a combination thereof. For example, these modules may be installed inpersistent storage device 352, loaded into memory 351, and executed byone or more processors (not shown). Note that some or all of thesemodules may be communicatively coupled to or integrated with some or allmodules of vehicle control system 111 of FIG. 2. Some of modules 301-309may be integrated together as an integrated module.

Localization module 301 determines a current location of autonomousvehicle 300 (e.g., leveraging GPS unit 212) and manages any data relatedto a trip or route of a user. Localization module 301 (also referred toas a map and route module) manages any data related to a trip or routeof a user. A user may log in and specify a starting location and adestination of a trip, for example, via a user interface. Localizationmodule 301 communicates with other components of autonomous vehicle 300,such as map and route information 311, to obtain the trip related data.For example, localization module 301 may obtain location and routeinformation from a location server and a map and POI (MPOI) server. Alocation server provides location services and an MPOI server providesmap services and the POIs of certain locations, which may be cached aspart of map and route information 311. While autonomous vehicle 300 ismoving along the route, localization module 301 may also obtainreal-time traffic information from a traffic information system orserver.

Based on the sensor data provided by sensor system 115 and localizationinformation obtained by localization module 301, a perception of thesurrounding environment is determined by perception module 302. Theperception information may represent what an ordinary driver wouldperceive surrounding a vehicle in which the driver is driving. Theperception can include the lane configuration, traffic light signals, arelative position of another vehicle, a pedestrian, a building,crosswalk, or other traffic related signs (e.g., stop signs, yieldsigns), etc., for example, in a form of an object. The laneconfiguration includes information describing a lane or lanes, such as,for example, a shape of the lane (e.g., straight or curvature), a widthof the lane, how many lanes in a road, one-way or two-way lane, mergingor splitting lanes, exiting lane, etc.

Perception module 302 may include a computer vision system orfunctionalities of a computer vision system to process and analyzeimages captured by one or more cameras in order to identify objectsand/or features in the environment of autonomous vehicle. The objectscan include traffic signals, road way boundaries, other vehicles,pedestrians, and/or obstacles, etc. The computer vision system may usean object recognition algorithm, video tracking, and other computervision techniques. In some embodiments, the computer vision system canmap an environment, track objects, and estimate the speed of objects,etc. Perception module 302 can also detect objects based on othersensors data provided by other sensors such as a radar and/or LIDAR.

For each of the objects, prediction module 303 predicts what the objectwill behave under the circumstances. The prediction is performed basedon the perception data perceiving the driving environment at the pointin time in view of a set of map/rout information 311 and traffic rules312. For example, if the object is a vehicle at an opposing directionand the current driving environment includes an intersection, predictionmodule 303 will predict whether the vehicle will likely move straightforward or make a turn. If the perception data indicates that theintersection has no traffic light, prediction module 303 may predictthat the vehicle may have to fully stop prior to enter the intersection.If the perception data indicates that the vehicle is currently at aleft-turn only lane or a right-turn only lane, prediction module 303 maypredict that the vehicle will more likely make a left turn or right turnrespectively.

For each of the objects, decision module 304 makes a decision regardinghow to handle the object. For example, for a particular object (e.g.,another vehicle in a crossing route) as well as its metadata describingthe object (e.g., a speed, direction, turning angle), decision module304 decides how to encounter the object (e.g., overtake, yield, stop,pass). Decision module 304 may make such decisions according to a set ofrules such as traffic rules or driving rules 312, which may be stored inpersistent storage device 352.

Routing module 307 is configured to provide one or more routes or pathsfrom a starting point to a destination point. For a given trip from astart location to a destination location, for example, received from auser, routing module 307 obtains route and map information 311 anddetermines all possible routes or paths from the starting location toreach the destination location. Routing module 307 may generate areference line in a form of a topographic map for each of the routes itdetermines from the starting location to reach the destination location.A reference line refers to an ideal route or path without anyinterference from others such as other vehicles, obstacles, or trafficcondition. That is, if there is no other vehicle, pedestrians, orobstacles on the road, an ADV should exactly or closely follows thereference line. The topographic maps are then provided to decisionmodule 304 and/or planning module 305. Decision module 304 and/orplanning module 305 examine all of the possible routes to select andmodify one of the most optimal routes in view of other data provided byother modules such as traffic conditions from localization module 301,driving environment perceived by perception module 302, and trafficcondition predicted by prediction module 303. The actual path or routefor controlling the ADV may be close to or different from the referenceline provided by routing module 307 dependent upon the specific drivingenvironment at the point in time.

Based on a decision for each of the objects perceived, planning module305 plans a path or route for the autonomous vehicle, as well as drivingparameters (e.g., distance, speed, and/or turning angle), using areference line provided by routing module 307 as a basis. That is, for agiven object, decision module 304 decides what to do with the object,while planning module 305 determines how to do it. For example, for agiven object, decision module 304 may decide to pass the object, whileplanning module 305 may determine whether to pass on the left side orright side of the object. Planning and control data is generated byplanning module 305 including information describing how vehicle 300would move in a next moving cycle (e.g., next route/path segment). Forexample, the planning and control data may instruct vehicle 300 to move10 meters at a speed of 30 mile per hour (mph), then change to a rightlane at the speed of 25 mph.

As part of the planning process, the path planner 309 may generate aplurality of planned ADV states based on a cost function 313, which maybe stored in persistent storage device 352.

Based on the planning and control data, control module 306 controls anddrives the autonomous vehicle, by sending proper commands or signals tovehicle control system 111, according to a route or path defined by theplanning and control data. The planning and control data includesufficient information to drive the vehicle from a first point to asecond point of a route or path using appropriate vehicle settings ordriving parameters (e.g., throttle, braking, steering commands) atdifferent points in time along the path or route.

In one embodiment, the planning phase is performed in a number ofplanning cycles, also referred to as driving cycles, such as, forexample, in every time interval of 100 milliseconds (ms). For each ofthe planning cycles or driving cycles, one or more control commands willbe issued based on the planning and control data. That is, for every 100ms, planning module 305 plans a next route segment or path segment, forexample, including a target position and the time required for the ADVto reach the target position. Alternatively, planning module 305 mayfurther specify the specific speed, direction, and/or steering angle,etc. In one embodiment, planning module 305 plans a route segment orpath segment for the next predetermined period of time such as 5seconds. For each planning cycle, planning module 305 plans a targetposition for the current cycle (e.g., next 5 seconds) based on a targetposition planned in a previous cycle. Control module 306 then generatesone or more control commands (e.g., throttle, brake, steering controlcommands) based on the planning and control data of the current cycle.

Note that decision module 304 and planning module 305 may be integratedas an integrated module. Decision module 304/planning module 305 mayinclude a navigation system or functionalities of a navigation system todetermine a driving path for the autonomous vehicle. For example, thenavigation system may determine a series of speeds and directionalheadings to affect movement of the autonomous vehicle along a path thatsubstantially avoids perceived obstacles while generally advancing theautonomous vehicle along a roadway-based path leading to an ultimatedestination. The destination may be set according to user inputs viauser interface system 113. The navigation system may update the drivingpath dynamically while the autonomous vehicle is in operation. Thenavigation system can incorporate data from a GPS system and one or moremaps so as to determine the driving path for the autonomous vehicle.

In one embodiment, paths are planned in an SL-coordinate system. TheSL-coordinate system may be defined relative to the reference line(road/lane center line). The longitudinal distance, or s-distance,represents the distance along the tangential direction of the referenceline. Correspondingly, the lateral distance, or 1-distance, representsthe distance perpendicular to the s-direction. The longitudinaldimension in the SL space represents a longitudinal distance of aparticular object from a current location of the vehicle that ispresumably drives along the reference line. The lateral dimension in theSL space represents the shortest distance between the object and thereference line at a particular time or location represented by thelongitudinal dimension. Such a graph in the SL space is referred to asan SL graph. In one embodiment, the lateral distance may be simplydefined as the distance from the reference line. Therefore, in additionto representation in the Cartesian coordinate system (XY plane), avehicle position (pose) may be represented in the SL-coordinate systemas an ordered pair (longitudinal pose/position “s-pose”, lateralpose/position “1-pose”), or simply (s, 1), with respect to a referenceline.

Referring to FIG. 4, a diagram 400 illustrating a vehicle position underan SL-coordinate system under an XY plane according to one embodiment isshown. The vehicle 410 has a position (x, y) in the 2D Cartesiancoordinate system. Additionally, the vehicle 410 position may also berepresented as (s, 1) under an SL-coordinate system defined with respectto a reference line 420.

Accordingly, it should be appreciated that in one embodiment, a path canbe represented in the SL-coordinate system using a function/(s),where/is the lateral distance to the reference line 420, and s is thelongitudinal distance, which is the accumulated distance along thetangential direction of the reference line 420.

In one embodiment, the comfort level associated with the path may bemodeled using the first and second derivatives of the lateral distancewith respect to the longitudinal distance, e.g.,

${\overset{.}{l} = \frac{dl}{ds}},{\overset{¨}{l} = {d^{2}l\text{/}{{ds}^{2}.}}}$They are analogous to the lateral velocity and lateral acceleration,which are the derivatives with respect to time instead. Hereinafter

${\overset{.}{l} = \frac{dl}{ds}},$which is a rate of change of the lateral distance with respect to changein the longitudinal distance, may be referred to as a first orderlateral rate of change, and {umlaut over (l)}=d²l/ds², which is a rateof change of the first order lateral rate of change with respect tochange in the longitudinal distance, may be referred to as a secondorder lateral rate of change. In one embodiment, a vehicle state at anylongitudinal distance may be represented with a triplet (l, {dot over(l)}, {umlaut over (l)}). Moreover, the lateral jerk of the vehicle maybe represented as

${\overset{...}{l}}_{iarrow{i - 1}} = {{( {{\overset{..}{l}}_{i} - {\overset{..}{l}}_{i - 1}} )/\Delta}{s.}}$The meaning of i and Δs will be explained in detail below.

In one embodiment, the comfort level associated with the path may bemodeled using the first and second derivatives of the longitudinaldistance with respect to time, e.g.,

${\overset{.}{m} = \frac{ds}{dt}},{\overset{¨}{m} = {d^{2}{s/d}t^{2}}}$They are analogous to the longitudinal velocity and longitudinalacceleration. Hereinafter

${{\overset{.}{m}*\overset{.}{l}} = \frac{dl}{dt}},$which is a rate of change of the lateral distance with respect to changein the time, may be referred to as a first order lateral rate of change(e.g., longitudinal velocity).

Besides comfort, other factors affect the desirability of the path aswell. The closeness to the reference line is one such factor since thevehicle needs to stay at the center of the road/lane if possible.Another factor is the distance to surrounding obstacles. The vehicleneeds to keep a certain buffer to account for potential perceptionerrors (e.g., errors or inaccuracies due to sensor data).

A further factor may be the longitudinal velocity (e.g., speed) of theADV. The longitudinal velocity may affect the comfort of the passengersin the ADV and/or the desirability of the path. For example, a path thathas both a high longitudinal velocity and a high lateral velocity forthe ADV may not be as desirable because the path may not be as safeand/or may not be as comfortable for the passengers of the ADV.

Referring to FIG. 5, a diagram illustrating an example method 500 forobtaining discretized obstacle boundaries under the SL-coordinate systemaccording to one embodiment is shown. The method 500 may be performed bya static obstacle mapper, which can be implemented in hardware,software, or a combination of both. Discretized points are chosen alongthe length of the reference line 510 under consideration, including thepoints at the beginning of the reference line 510 under consideration(e.g., s=0) and at the end (e.g., s=s_(max)), where any two adjacentdiscretized points are spaced by a uniform longitudinal distance,referred to as a longitudinal distance discretization resolution Δs.

In other words, the discretized points are located at s=0, Δs, 2Δs, 3Δs,. . . , s_(max). The position and geometry of static obstacles areknown. For each static obstacle that overlaps in the longitudinaldistance with any of the discretized points, two lateral distances—onecorresponding to the upper boundary and one corresponding to the lowerboundary—at the overlapping longitudinal distance are obtained. Forexample, the static obstacle 520 overlaps in the longitudinal distancewith two discretized points (one at s=Δs, and the other at s=2Δs). Atthe longitudinal distance s=Δs, one upper boundary lateral distance l₁^(U) and one lower boundary lateral distance l₁ ^(L) may be obtained forthe static obstacle 520. Similarly, one upper boundary lateral distancel₂ ^(U) and one lower boundary lateral distance l₂ ^(L) (not shown) maybe obtained for the static obstacle 520 at the longitudinal distances=2Δs. In other words, by utilizing the method 500 described above,∀i∈[0, N] (for any i that is between 0 and N, inclusive), the mappings_(i)→(l_(i) ^(L), l_(i) ^(U)) may be obtained, where N=s_(max)/Δs, ands_(i)=i*Δs.

In one embodiment, the path planner 309 receives one or more inputs, andgenerates one or more path outputs under one or more constraints, wherethe path outputs are values of path variables that minimize the value ofa cost function associated with one or more path objectives.

In one embodiment, inputs to the path planner may comprise: 1) a lateralstarting state (l₀, {dot over (l)}₀, {umlaut over (l)}₀) (e.g., thevehicle lateral state

$ { {{( {l,\ \overset{.}{l},\ \overset{¨}{l}}\; )\; s} = 0} );2} )$a threshold lateral jerk (lateral jerk limit)

$ {{{\overset{...}{l}}_{\max}( {{\overset{...}{l}}_{\max} > 0} )};3} )$static obstacle boundaries with respect to the reference line (e.g., inthe SL-coordinate system); 4) a longitudinal starting state (m₀,{dotover (m)}₀, {umlaut over (m)}₀) (e.g., the vehicle longitudinal state(m, {dot over (m)}, {umlaut over (m)}) at s=0); 5) a threshold lateralvelocity d_(max)

$( {{e.g.},\frac{dl}{dt}} );$and 6) an optional target vehicle ending state (l_(e), {dot over(l)}_(e), {umlaut over (l)}_(e)). In some embodiments, the functionalityof the static obstacle mapper may be incorporated into that of the pathplanner. Therefore, inputs to the path planner may not include thestatic obstacle boundaries with respect to the reference line (e.g., inthe SL-coordinate system), but may further comprise: 7) a longitudinallength of the reference line under consideration s_(max); 8) alongitudinal distance discretization resolution Δs; and 9) the positionand geometry of static obstacles within the longitudinal distance range(0, s_(max)).

The path variables may be the vehicle state (l, {dot over (l)}, {umlautover (l)}) at each longitudinal distance that corresponds to adiscretized point along the reference line after the starting point ofthe reference line up to the end point of the reference line underconsideration. In other words, the path variables may comprise: (l₁,{dot over (l)}₁, {umlaut over (l)}₁) (e.g., the vehicle state at s=1Δs),(l₂, {dot over (l)}₂, {umlaut over (l)}₂) (e.g., the vehicle state ats=2Δs), etc., including all the intervening vehicle states up to theending state at the end point of the reference line under consideration(l_(N), {dot over (l)}_(N), {umlaut over (l)}_(N)) (e.g., the vehiclestate at s=s_(max)=NΔs).

In one embodiment, the path planner operates under the followingequality constraints. The first equality constraint may be defined asfollows:

${\forall{i \in \lbrack {1_{,}N} \rbrack}},{{\overset{...}{l}}_{iarrow{i - 1}} = {{( {{\overset{¨}{l}}_{i} - {\overset{¨}{l}}_{i - 1}} )/\Delta}{s.}}}$The second equality constraint may be defined as follows:

${\forall{i \in \lbrack {1_{1}N} \rbrack}},{{\overset{.}{l}}_{i} = {{\overset{.}{l}}_{i - 1} + {{\overset{¨}{l}}_{i - 1}*{\Delta s}} + {{1/2}*{\overset{...}{l}}_{iarrow{i - 1}}*\Delta{s^{2}.}}}}$The third equality constraint may be defined as follows:

${\forall{i \in \lbrack {1,\ N} \rbrack}},{l_{i} = {l_{i - 1} + {{\overset{.}{l}}_{i - 1}*\Delta s} + {{1/2}*{\overset{¨}{l}}_{i - 1}*\Delta s^{2}} + {{1/6}*{\overset{...}{l}}_{iarrow{i - 1}}*\Delta{s^{3}.}}}}$It should be appreciated that the equality constraints 1) through 3)ensure that from one discretized point to the next (e.g., one Δs to thenext), the correct mathematical relationships among

$l_{i},{\overset{.}{l}}_{i},{\overset{...}{l}}_{iarrow{i - 1}},l_{i - 1},{{and}\mspace{14mu}{\overset{.}{l}}_{i - 1}}$are maintained. Further, in cases where the optional target vehicleending state (l_(e), {dot over (l)}_(e), {umlaut over (l)}_(e)) issupplied as an input, the path planner may operate under a furtherequality constraint which may be defined as follows:

${l_{N} = l_{e}},{{\overset{.}{l}}_{N} = {\overset{.}{l}}_{e}},{{\overset{.}{l}}_{N} = {\overset{¨}{l}}_{e}},$which ensures that the vehicle state (l_(N), {dot over (l)}_(N), {umlautover (l)}_(N)) at s=s_(max) matches the specified target vehicle endingstate (l_(e), {dot over (l)}_(e), {umlaut over (l)}_(e)). An equalityconstraint may be referred to as a path constraint.

In one embodiment, the path planner operates under the followinginequality constraints. The first inequality constraint may be definedas follows:

${{\forall{i \in \lbrack {1,N} \rbrack}},{{\overset{...}{l}}_{iarrow{i - 1}} \in {\lbrack {{- {\overset{...}{l}}_{\max}},{\overset{...}{l}}_{\max}} \rbrack.}}}\mspace{79mu}$The first inequality constraint may help prevent the lateral jerk

${\overset{...}{l}}_{iarrow{i - 1}}$of the ADV from exceeding the threshold lateral jerk

${\overset{...}{l}}_{m\;{ax}}$in either direction. For example, if the lateral jerk

${\overset{...}{l}}_{iarrow{i - 1}}$of the ADV does not exceed the threshold lateral jerk

${\overset{...}{l}}_{m\;{ax}}$in either direction, the first inequality constraint may be satisfied ormet. The second inequality constraint may be defined as follows:

∀i ∈ [1, N], l_(i) ∈ (l_(i)^(L), l_(i)^(U)),which ensures that the vehicle does not collide with any staticobstacles. The third inequality constraint may be defined as follows:

${\forall{i \in \lbrack {1,N} \rbrack}},{{{\overset{.}{l}}_{i}*{\overset{.}{m}}_{i}} \in {\lbrack {{- d_{\max}},\ d_{\max}} \rbrack.}}$An inequality constraint may be referred to as a path constraint.

In one embodiment, the third inequality constraint may use or include afunction (e.g., an equation, a formula, etc.) that may be referred to asa speed function. The speed function may be defined as: {dot over(l)}_(i)*{dot over (m)}_(i), where {dot over (l)}_(i) is the lateralvelocity of the ADV and {dot over (m)}_(i) is the longitudinal velocityof the ADV. The third inequality constraint may be met or satisfied whenthe product of the lateral velocity and the longitudinal velocity of theADV is less than the threshold lateral velocity d_(max). Although amultiplication operation is disclosed herein, the speed function may useother operations (e.g., addition, subtraction, etc.) in otherembodiments.

In one embodiment, the third inequality constraint may define an inverserelationship between the lateral velocity and the longitudinal velocityof the ADV. If the lateral velocity is higher, the longitudinal velocitymay be lower because the product of the lateral velocity and thelongitudinal velocity of the ADV should be less than the thresholdlateral velocity d_(max) to satisfy the third inequality constraint, andvice versa. Thus, the path planner 309 may generate or determine a paththat has a lower lateral velocity when the longitudinal velocity ishigher, and may generate or determine a path that has a higher lateralvelocity when the longitudinal velocity is lower.

In one embodiment, the cost function associated with the objectives andto be minimized may be w₀*Σ₁ ^(N)l_(i) ²+w₁*Σ₁ ^(N){dot over (l)}_(i)^({dot over (2)})+w₂*Σ₁ ^(N){umlaut over (l)}_(i) ^({dot over (2)}),where w₀, w₁, and w₂ are weights that can be determined empirically.Therefore, it should be appreciated that by minimizing the costfunction, the optimization yields, within the confines of the inputs andconstraints, outputs that minimize the cumulative lateral distances, thecumulative first order lateral rates of change, and the cumulativesecond order lateral rates of change. In other words, the optimizationyields a path that is close to the reference line and is associated witha high level of comfort. The relative importance of minimizing any ofthe three cumulative values is controlled by the weights w₀, w₁, and w₂.

Referring to FIG. 6, a block diagram 600 illustrating various examplecomponents involved in the optimization process according to oneembodiment is shown. In one embodiment, the static obstacle mapper 308and the path planner 309 may be integrated into the planning module 305of FIGS. 3A and 3B. The static obstacle mapper 308 generates staticobstacle boundaries and maps the obstacle onto an SL space, which may bepassed onto the path planner as inputs. The path planner 309 receivesinputs 620, constraints 630, path variables 640, and a cost function 313associated with path objectives. The path planner 309 performs nonlinear(quadratic) optimization, and yields path results 660, which are valuesof path variables 640 that minimize the value of the cost function 313.Nonlinear optimization is well-known in the art, and therefore is notdescribed in further detail herein. The static obstacle mapper 308 andpath planner 309 may be implemented in hardware, software, or acombination of both. As described above, in some embodiments, the staticobstacle mapper 308 may be further integrated into the path planner 309.

Referring to FIG. 7, a flowchart illustrating an example method 700 forplanning an optimal path at an ADV according to one embodiment is shown.The method 700 may be performed by hardware, software, or a combinationof both. At block 710, a plurality of path inputs may be obtained, theplurality of path inputs comprising an autonomous driving vehicle (ADV)starting state, a threshold lateral jerk, and static obstacle boundarieswith respect to a reference line. At block 720, a plurality of pathconstraints may be obtained, the plurality of path constraintscomprising constraints relating to the threshold lateral jerk andavoidance of one or more static obstacles. At block 730, a cost functionassociated with an path objective may be obtained, the cost functioncomprising a first term relating to cumulative lateral distances, asecond term relating to cumulative first order lateral rates of change,and a third term relating to cumulative second order lateral rates ofchange. At block 740, a plurality of planned ADV states may be generatedas path results with nonlinear optimization, wherein the path resultsminimize a value of the cost function. At block 750, control signals maybe generated to control the ADV based on the plurality of planned ADVstates.

Referring to FIG. 8, a diagram illustrating an example method 800 fordetermining a path for an ADV 805 under the SL-coordinate systemaccording to one embodiment is shown. The method 800 may be performed bypath planner 309, which can be implemented in hardware, software, or acombination of both. Discretized points are chosen along the length ofthe reference line 810 under consideration, including the points at thebeginning of the reference line 810 under consideration (e.g., s=0) andat the end (e.g., s=s_(max)), where any two adjacent discretized pointsare spaced by a uniform longitudinal distance, referred to as alongitudinal distance discretization resolution Δs. As illustrated inFIG. 8, the ADV 805 may not be traveling on the reference line 810(e.g., a reference path). The path planner 309 may determine a path thatmay move the ADV 805 closer to and/or back onto the reference line 810.The ADV 805 has a current longitudinal velocity {dot over (m)} or

$\frac{ds}{dt},$and a current lateral velocity {dot over (l)} or

$\frac{dl}{ds}.$

In one embodiment, the path planner 309 receives one or more inputs, andgenerates one or more path outputs under one or more constraints, wherethe path outputs are values of path variables that minimize the value ofa cost function associated with one or more path objectives. The pathinput may include a lateral starting state (l₀, {dot over (l)}₀, {umlautover (l)}₀), a threshold lateral jerk

${{\overset{...}{l}}_{\max}( {{\overset{...}{l}}_{\max} > 0} )},$static obstacle boundaries with respect to the reference line (e.g., inthe SL-coordinate system); a longitudinal starting state (m₀, {dot over(m)}₀, {umlaut over (m)}₀); 5) a threshold lateral velocity d_(max)

$( {{e.g.},\frac{dl}{dt}} );$and 6) an optional target vehicle ending state (l_(e), {dot over(l)}_(e), {umlaut over (l)}_(e)), as discussed above. The path variablesmay be the vehicle state (l, {dot over (l)}, {umlaut over (l)}) at eachlongitudinal distance that corresponds to a discretized point along thereference line after the starting point of the reference line up to theend point of the reference line under consideration.

In one embodiment, the path planner 309 operates under or using equalityconstraints and inequality constraints (e.g., path constraints), asdiscussed above. As discussed above, one of the inequality constraintsthat may be used by the path planner 309 may be define follows: ∀i ∈[1,N], {dot over (l)}_(i)*{dot over (m)}_(i) ∈[−d_(max), d_(max)]. Theinequality constraint may use or include a function (e.g., an equation,a formula, etc.) that may be referred to as a speed function which maybe defined as: {dot over (l)}_(i)*{dot over (m)}_(i), where {dot over(l)}_(i) is the lateral velocity of the ADV 805 and {dot over (m)}_(i)is the longitudinal velocity of the ADV. The inequality constraint maybe met or satisfied when the product of the lateral velocity and thelongitudinal velocity of the ADV is less than the threshold lateralvelocity d_(max), as discussed above. The inequality constraint maydefine an inverse relationship between the lateral velocity and thelongitudinal velocity of the ADV.

In one embodiment, the cost function associated with the objectives andto be minimized may be w₀*Σ₁ ^(N)l_(i) ²+w₁*Σ₁ ^(N){dot over (l)}_(i)^({dot over (2)})+w₂*Σ₁ ^(N){umlaut over (l)}_(i) ^({dot over (2)}),where w₀, w₁, and w₂ are weights that can be determined empirically.Therefore, it should be appreciated that by minimizing the costfunction, the optimization yields, within the confines of the inputs andconstraints, outputs that minimize the cumulative lateral distances, thecumulative first order lateral rates of change, and the cumulativesecond order lateral rates of change. For example, if the cost functionis minimized and the equality and inequality constraints (e.g., pathconstraints) are satisfied and/or met, the path planner 309 may be ableto determine a path for the ADV 800. In other words, the optimization ofthe cost function (e.g., minimizing the results of the cost function)may yield a path that is close to the reference line and is associatedwith a high level of comfort. The relative importance of minimizing anyof the three cumulative values is controlled by the weights w₀, w₁, andw₂.

Two example paths 821 and 822 are illustrated in FIG. 8. Paths 821 and822 start at the ADV 805 (e.g., have a starting point at the ADV 805).Path 821 ends on the path 810 between Δs and 2Δs. Path 822 ends on thepath 810 between 2Δs and 3Δs. Path 821 may be a path determined by thepath planner 309 when the longitudinal velocity

$\frac{ds}{dt},$of the ADV 805 is lower. Path 822 may be a path determine by the pathplanner 309 when the longitudinal velocity

$\frac{ds}{dt},$805 is higher. As discussed above, the inequality constraint may definean inverse relationship between the lateral velocity

$\frac{dl}{ds}.$and me longitudinal velocity

$\frac{ds}{dt},$of the ADV 805. When the longitudinal velocity is

$\frac{ds}{dt},$is higher (as illustrated in path 822), the lateral velocity

$\frac{dl}{ds}$may be lower. This may cause the path 822 to reach the reference line810 further down along the reference line 810 (when compared to path821) because the ADV 805 may move laterally (e.g., may move upwardstowards the reference line 810) more slowly. When the longitudinalvelocity is

$\frac{ds}{dt},$is lower (as illustrated in path 821), the lateral velocity

$\frac{dl}{ds}.$may be higher. This may cause the path 821 to reach the reference line810 earlier along the reference line 810 (when compared to path 822)because the ADV 805 may move laterally (e.g., may move upwards towardsthe reference line 810) more quickly.

Referring to FIG. 9, a flowchart illustrating an example method 900 forplanning a path for an ADV according to one embodiment is shown. Themethod 900 may be performed by hardware, software, or a combination ofboth. For example, the method 900 may be performed by planning module305, path planner 309, etc. At block 910, obtain the longitudinalvelocity of the ADV. For example, a plurality of path inputs may beobtained, the plurality of path inputs comprising an autonomous drivingvehicle (ADV) lateral starting state, an ADV longitudinal starting rate,a threshold lateral jerk, and static obstacle boundaries with respect toa reference line. The method 900 may obtain (e.g., read, access, etc.)the plurality of path inputs from a memory or may receive the pluralityof path inputs (e.g., from one or more sensors). At block 920, themethod 900 may obtain a threshold lateral velocity. For example, themethod 900 may obtain (e.g., read, access, etc.) the threshold lateralvelocity or may receive the threshold lateral velocity (e.g., receivethe threshold lateral velocity from a user). The threshold lateralvelocity may be a configurable setting or parameter in some embodiments(e.g., configurable by a user).

At block 930, the method 900 may determine a lateral velocity for theADV based on a path constraint. For example, the method 900 may use thethird inequality constraint discussed above in conjunction with FIG. 5.The path constraint (e.g., inequality constraint) may use a function(e.g., a speed function) that determines the lateral velocity of the ADVbased on the longitudinal velocity and the threshold lateral velocity.As discussed above, the longitudinal velocity of the ADV and the lateralvelocity of the ADV may have an inverse relationship due to the pathconstraint. For example, the path constraint may cause the lateralvelocity to be lower when the longitudinal velocity is higher, and viceversa.

At block 930 the method 900 may generate a plurality of planned ADVstates based on a cost function, a plurality of path inputs, and aplurality of path constraints. The cost function may include a firstterm relating to cumulative lateral distances, a second term relating tocumulative first order lateral rates of change, and a third termrelating to cumulative second order lateral rates of change. Theplurality of planned ADV states may be generated as path results withnonlinear optimization, wherein the path results minimize a value of thecost function while meeting or satisfying the plurality of pathconstraints. At block 950, control signals may be generated to controlthe ADV based on the plurality of planned ADV states. For example, theplurality of planned ADV states may define a path for the ADV and themethod may control the ADV based on the path (e.g., may cause the ADV tofollow or drive along the path).

In one embodiment, an SL-coordinate system comprising a longitudinaldimension and a lateral dimension may be utilized. The longitudinal (s)dimension is along a tangential direction of a reference line, and thelateral (1) dimension is perpendicular to the longitudinal dimension.Each of the ADV starting state and the plurality of planned ADV statesmay comprise a lateral distance, a first order lateral rate of change,and a second order lateral rate of change. The first order lateral rateof change is a rate of change of the lateral distance with respect tochange of longitudinal distance; further, the second order lateral rateof change is a rate of change of the first order lateral rate of changewith respect to change of longitudinal distance.

The cost function may further include a first weight (w₀) associatedwith the first term, a second weight (w₁) associated with the secondterm, and a third weight (w₂) associated with the third term. Theplurality of planned ADV states may correspond to discretized pointsalong the reference line spaced by a uniform longitudinal distancediscretization resolution (Δs) between a starting point of the referenceline under consideration (s=0) and an ending point (s=s_(max)). In oneembodiment, the plurality of path inputs may further comprise a targetADV ending state.

Note that some or all of the components as shown and described above maybe implemented in software, hardware, or a combination thereof. Forexample, such components can be implemented as software installed andstored in a persistent storage device, which can be loaded and executedin a memory by a processor (not shown) to carry out the processes oroperations described throughout this application. Alternatively, suchcomponents can be implemented as executable code programmed or embeddedinto dedicated hardware such as an integrated circuit (e.g., anapplication specific IC or ASIC), a digital signal processor (DSP), or afield programmable gate array (FPGA), which can be accessed via acorresponding driver and/or operating system from an application.Furthermore, such components can be implemented as specific hardwarelogic in a processor or processor core as part of an instruction setaccessible by a software component via one or more specificinstructions.

FIG. 10 is a block diagram illustrating an example of a data processingsystem which may be used with one embodiment of the disclosure. Forexample, system 1500 may represent any of data processing systemsdescribed above performing any of the processes or methods describedabove, such as, for example, perception and planning system 110 or anyof servers 103-104 of FIG. 1, and path planner 309 of FIG. 6. System1500 can include many different components. These components can beimplemented as integrated circuits (ICs), portions thereof, discreteelectronic devices, or other modules adapted to a circuit board such asa motherboard or add-in card of the computer system, or as componentsotherwise incorporated within a chassis of the computer system.

Note also that system 1500 is intended to show a high level view of manycomponents of the computer system. However, it is to be understood thatadditional components may be present in certain implementations andfurthermore, different arrangement of the components shown may occur inother implementations. System 1500 may represent a desktop, a laptop, atablet, a server, a mobile phone, a media player, a personal digitalassistant (PDA), a Smartwatch, a personal communicator, a gaming device,a network router or hub, a wireless access point (AP) or repeater, aset-top box, or a combination thereof. Further, while only a singlemachine or system is illustrated, the term “machine” or “system” shallalso be taken to include any collection of machines or systems thatindividually or jointly execute a set (or multiple sets) of instructionsto perform any one or more of the methodologies discussed herein.

In one embodiment, system 1500 includes processor 1501, memory 1503, anddevices 1505-1508 connected via a bus or an interconnect 1510. Processor1501 may represent a single processor or multiple processors with asingle processor core or multiple processor cores included therein.Processor 1501 may represent one or more general-purpose processors suchas a microprocessor, a central processing unit (CPU), or the like. Moreparticularly, processor 1501 may be a complex instruction set computing(CISC) microprocessor, reduced instruction set computing (RISC)microprocessor, very long instruction word (VLIW) microprocessor, orprocessor implementing other instruction sets, or processorsimplementing a combination of instruction sets. Processor 1501 may alsobe one or more special-purpose processors such as an applicationspecific integrated circuit (ASIC), a cellular or baseband processor, afield programmable gate array (FPGA), a digital signal processor (DSP),a network processor, a graphics processor, a communications processor, acryptographic processor, a co-processor, an embedded processor, or anyother type of logic capable of processing instructions.

Processor 1501, which may be a low power multi-core processor socketsuch as an ultra-low voltage processor, may act as a main processingunit and central hub for communication with the various components ofthe system. Such processor can be implemented as a system on chip (SoC).Processor 1501 is configured to execute instructions for performing theoperations and steps discussed herein. System 1500 may further include agraphics interface that communicates with optional graphics subsystem1504, which may include a display controller, a graphics processor,and/or a display device.

Processor 1501 may communicate with memory 1503, which in one embodimentcan be implemented via multiple memory devices to provide for a givenamount of system memory. Memory 1503 may include one or more volatilestorage (or memory) devices such as random access memory (RAM), dynamicRAM (DRAM), synchronous DRAM (SDRAM), static RAM (SRAM), or other typesof storage devices. Memory 1503 may store information includingsequences of instructions that are executed by processor 1501, or anyother device. For example, executable code and/or data of a variety ofoperating systems, device drivers, firmware (e.g., input output basicsystem or BIOS), and/or applications can be loaded in memory 1503 andexecuted by processor 1501. An operating system can be any kind ofoperating systems, such as, for example, Robot Operating System (ROS),Windows® operating system from Microsoft®, Mac OS®/iOS® from Apple,Android® from Google®, LINUX, UNIX, or other real-time or embeddedoperating systems.

System 1500 may further include IO devices such as devices 1505-1508,including network interface device(s) 1505, optional input device(s)1506, and other optional IO device(s) 1507. Network interface device1505 may include a wireless transceiver and/or a network interface card(NIC). The wireless transceiver may be a WiFi transceiver, an infraredtransceiver, a Bluetooth transceiver, a WiMax transceiver, a wirelesscellular telephony transceiver, a satellite transceiver (e.g., a globalpositioning system (GPS) transceiver), or other radio frequency (RF)transceivers, or a combination thereof. The NIC may be an Ethernet card.

Input device(s) 1506 may include a mouse, a touch pad, a touch sensitivescreen (which may be integrated with display device 1504), a pointerdevice such as a stylus, and/or a keyboard (e.g., physical keyboard or avirtual keyboard displayed as part of a touch sensitive screen). Forexample, input device 1506 may include a touch screen controller coupledto a touch screen. The touch screen and touch screen controller can, forexample, detect contact and movement or break thereof using any of aplurality of touch sensitivity technologies, including but not limitedto capacitive, resistive, infrared, and surface acoustic wavetechnologies, as well as other proximity sensor arrays or other elementsfor determining one or more points of contact with the touch screen.

IO devices 1507 may include an audio device. An audio device may includea speaker and/or a microphone to facilitate voice-enabled functions,such as voice recognition, voice replication, digital recording, and/ortelephony functions. Other IO devices 1507 may further include universalserial bus (USB) port(s), parallel port(s), serial port(s), a printer, anetwork interface, a bus bridge (e.g., a PCI-PCI bridge), sensor(s)(e.g., a motion sensor such as an accelerometer, gyroscope, amagnetometer, a light sensor, compass, a proximity sensor, etc.), or acombination thereof. Devices 1507 may further include an imagingprocessing subsystem (e.g., a camera), which may include an opticalsensor, such as a charged coupled device (CCD) or a complementarymetal-oxide semiconductor (CMOS) optical sensor, utilized to facilitatecamera functions, such as recording photographs and video clips. Certainsensors may be coupled to interconnect 1510 via a sensor hub (notshown), while other devices such as a keyboard or thermal sensor may becontrolled by an embedded controller (not shown), dependent upon thespecific configuration or design of system 1500.

To provide for persistent storage of information such as data,applications, one or more operating systems and so forth, a mass storage(not shown) may also couple to processor 1501. In various embodiments,to enable a thinner and lighter system design as well as to improvesystem responsiveness, this mass storage may be implemented via a solidstate device (SSD). However in other embodiments, the mass storage mayprimarily be implemented using a hard disk drive (HDD) with a smalleramount of SSD storage to act as a SSD cache to enable non-volatilestorage of context state and other such information during power downevents so that a fast power up can occur on re-initiation of systemactivities. Also a flash device may be coupled to processor 1501, e.g.,via a serial peripheral interface (SPI). This flash device may providefor non-volatile storage of system software, including BIOS as well asother firmware of the system.

Storage device 1508 may include computer-accessible storage medium 1509(also known as a machine-readable storage medium or a computer-readablemedium) on which is stored one or more sets of instructions or software(e.g., module, unit, and/or logic 1528) embodying any one or more of themethodologies or functions described herein. Processingmodule/unit/logic 1528 may represent any of the components describedabove, such as, for example, planning module 305, control module 306,and path planner 309. Processing module/unit/logic 1528 may also reside,completely or at least partially, within memory 1503 and/or withinprocessor 1501 during execution thereof by data processing system 1500,memory 1503 and processor 1501 also constituting machine-accessiblestorage media. Processing module/unit/logic 1528 may further betransmitted or received over a network via network interface device1505.

Computer-readable storage medium 1509 may also be used to store the somesoftware functionalities described above persistently. Whilecomputer-readable storage medium 1509 is shown in an exemplaryembodiment to be a single medium, the term “computer-readable storagemedium” should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. The terms“computer-readable storage medium” shall also be taken to include anymedium that is capable of storing or encoding a set of instructions forexecution by the machine and that cause the machine to perform any oneor more of the methodologies of the present disclosure. The term“computer-readable storage medium” shall accordingly be taken toinclude, but not be limited to, solid-state memories, and optical andmagnetic media, or any other non-transitory machine-readable medium.

Processing module/unit/logic 1528, components and other featuresdescribed herein can be implemented as discrete hardware components orintegrated in the functionality of hardware components such as ASICS,FPGAs, DSPs or similar devices. In addition, processingmodule/unit/logic 1528 can be implemented as firmware or functionalcircuitry within hardware devices. Further, processing module/unit/logic1528 can be implemented in any combination hardware devices and softwarecomponents.

Note that while system 1500 is illustrated with various components of adata processing system, it is not intended to represent any particulararchitecture or manner of interconnecting the components; as suchdetails are not germane to embodiments of the present disclosure. Itwill also be appreciated that network computers, handheld computers,mobile phones, servers, and/or other data processing systems which havefewer components or perhaps more components may also be used withembodiments of the disclosure.

Some portions of the preceding detailed descriptions have been presentedin terms of algorithms and symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptions andrepresentations are the ways used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of operations leading to adesired result. The operations are those requiring physicalmanipulations of physical quantities.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as those set forth in the claims below, refer to the actionand processes of a computer system, or similar electronic computingdevice, that manipulates and transforms data represented as physical(electronic) quantities within the computer system's registers andmemories into other data similarly represented as physical quantitieswithin the computer system memories or registers or other suchinformation storage, transmission or display devices.

Embodiments of the disclosure also relate to an apparatus for performingthe operations herein. Such a computer program is stored in anon-transitory computer readable medium. A machine-readable mediumincludes any mechanism for storing information in a form readable by amachine (e.g., a computer). For example, a machine-readable (e.g.,computer-readable) medium includes a machine (e.g., a computer) readablestorage medium (e.g., read only memory (“ROM”), random access memory(“RAM”), magnetic disk storage media, optical storage media, flashmemory devices).

The processes or methods depicted in the preceding figures may beperformed by processing logic that comprises hardware (e.g. circuitry,dedicated logic, etc.), software (e.g., embodied on a non-transitorycomputer readable medium), or a combination of both. Although theprocesses or methods are described above in terms of some sequentialoperations, it should be appreciated that some of the operationsdescribed may be performed in a different order. Moreover, someoperations may be performed in parallel rather than sequentially.

Embodiments of the present disclosure are not described with referenceto any particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof embodiments of the disclosure as described herein.

In the foregoing specification, embodiments of the disclosure have beendescribed with reference to specific exemplary embodiments thereof. Itwill be evident that various modifications may be made thereto withoutdeparting from the broader spirit and scope of the disclosure as setforth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

What is claimed is:
 1. A computer-implemented method, comprising:obtaining a plurality of path inputs comprising a lateral starting statefor an autonomous driving vehicle (ADV), a longitudinal starting statefor the ADV, a threshold lateral jerk, and a set of static obstacleboundaries with respect to a reference line; obtaining a plurality ofpath constraints comprising a first constraint related to the thresholdlateral jerk, a second constraint related to avoidance of one or morestatic obstacles, and a third constraint related to a threshold lateralvelocity; obtaining a cost function associated with a path objective,the cost function comprising a first term relating to cumulative lateraldistances, a second term relating to cumulative first order lateralrates of change, and a third term relating to cumulative second orderlateral rates of change; generating a plurality of planned ADV states aspath results based on the plurality of path inputs, the plurality ofpath constraints, and the cost function, wherein the path resultsminimize a value of the cost function; and generating one or morecontrol signals to control the ADV based on the plurality of planned ADVstates.
 2. The method of claim 1, wherein each of the lateral startingstate and the plurality of planned ADV states comprises a lateraldistance, a first order lateral rate of change, and a second orderlateral rate of change.
 3. The method of claim 2, wherein the firstorder lateral rate of change is a rate of change of the lateral distancewith respect to change of longitudinal distance, and wherein the secondorder lateral rate of change is a rate of change of the first orderlateral rate of change with respect to change of longitudinal distance.4. The method of claim 1, wherein the longitudinal starting statecomprises a longitudinal distance, a first order longitudinal rate ofchange, and a second order longitudinal rate of change.
 5. The method ofclaim 4, wherein the first order longitudinal rate of change is a rateof change of the longitudinal distance with respect to change of time,and wherein the second order longitudinal rate of change is a rate ofchange of the first order longitudinal rate of change with respect tochange of time.
 6. The method of claim 1, wherein the plurality ofinputs further comprises the threshold lateral velocity.
 7. The methodof claim 1, wherein the path results satisfy the plurality ofconstraints.
 8. The method of claim 1, wherein generating the pluralityof planned ADV states comprises: determining a lateral speed based on aspeed function, a first order longitudinal rate of change, and the firstorder lateral rate of change, wherein the lateral speed satisfies thethird constraint related to the threshold lateral velocity.
 9. Themethod of claim 1, wherein the cost function further comprises a firstweight associated with the first term, a second weight associated withthe second term, and a third weight associated with the third term. 10.The method of claim 1, wherein the plurality of planned ADV statescorrespond to discretized points along the reference line spaced by auniform longitudinal distance discretization resolution between abeginning point and an ending point of the reference line.
 11. Themethod of claim 1, wherein the plurality of path inputs furthercomprises a target ADV ending state.
 12. The method of claim 1, whereinan SL-coordinate system comprising a longitudinal dimension and alateral dimension is utilized, wherein the longitudinal dimension isalong a tangential direction of the reference line, and wherein thelateral dimension is perpendicular to the longitudinal dimension.
 13. Anon-transitory machine-readable medium having instructions storedtherein, which when executed by a processor, cause the processor toperform operations, the operations comprising: obtaining a plurality ofpath inputs comprising a lateral starting state for an autonomousdriving vehicle (ADV), a longitudinal starting state for the ADV, athreshold lateral jerk, and a set of static obstacle boundaries withrespect to a reference line; obtaining a plurality of path constraintscomprising a first constraint related to the threshold lateral jerk, asecond constraint related to avoidance of one or more static obstacles,and a third constraint related to a threshold lateral velocity;obtaining a cost function associated with a path objective, the costfunction comprising a first term relating to cumulative lateraldistances, a second term relating to cumulative first order lateralrates of change, and a third term relating to cumulative second orderlateral rates of change; generating a plurality of planned ADV states aspath results based on the plurality of path inputs, the plurality ofpath constraints, and the cost function, wherein the path resultsminimize a value of the cost function; and generating one or morecontrol signals to control the ADV based on the plurality of planned ADVstates.
 14. The non-transitory machine-readable medium of claim 13,wherein each of the lateral starting state and the plurality of plannedADV states comprises a lateral distance, a first order lateral rate ofchange, and a second order lateral rate of change.
 15. Thenon-transitory machine-readable medium of claim 14, wherein the firstorder lateral rate of change is a rate of change of the lateral distancewith respect to change of longitudinal distance, and wherein the secondorder lateral rate of change is a rate of change of the first orderlateral rate of change with respect to change of longitudinal distance.16. The non-transitory machine-readable medium of claim 13, wherein thelongitudinal starting state comprises a longitudinal distance, a firstorder longitudinal rate of change, and a second order longitudinal rateof change.
 17. The non-transitory machine-readable medium of claim 16,wherein the first order longitudinal rate of change is a rate of changeof the longitudinal distance with respect to change of time, and whereinthe second order longitudinal rate of change is a rate of change of thefirst order longitudinal rate of change with respect to change of time.18. The non-transitory machine-readable medium of claim 13, whereingenerating the plurality of planned ADV states comprises: determining alateral speed based on a speed function, a first order longitudinal rateof change, and the first order lateral rate of change, wherein thelateral speed satisfies the third constraint related to the thresholdlateral velocity.
 19. The non-transitory machine-readable medium ofclaim 13, wherein the cost function further comprises a first weightassociated with the first term, a second weight associated with thesecond term, and a third weight associated with the third term.
 20. Adata processing system, comprising: a processor; and a memory coupled tothe processor to store instructions, which when executed by theprocessor, cause the processor to perform operations, the operationsincluding: obtaining a plurality of path inputs comprising a lateralstarting state for an autonomous driving vehicle (ADV), a longitudinalstarting state for the ADV, a threshold lateral jerk, and a set ofstatic obstacle boundaries with respect to a reference line; obtaining aplurality of path constraints comprising a first constraint related tothe threshold lateral jerk, a second constraint related to avoidance ofone or more static obstacles, and a third constraint related to athreshold lateral velocity; obtaining a cost function associated with apath objective, the cost function comprising a first term relating tocumulative lateral distances, a second term relating to cumulative firstorder lateral rates of change, and a third term relating to cumulativesecond order lateral rates of change; generating a plurality of plannedADV states as path results based on the plurality of path inputs, theplurality of path constraints, and the cost function, wherein the pathresults minimize a value of the cost function; and generating one ormore control signals to control the ADV based on the plurality ofplanned ADV states.